I am going through Sean Carroll's Spacetime and Geometry, trying to learn GR. On page 31, he introduces the concept of the four-velocity $U^\mu$ as $$U^\mu = \frac{dx^\mu}{d\tau}$$ where $\tau$ is the proper time along a timelike path, with a timelike interval given by $$d{\tau}^2 = -\eta_{\mu\up...

While I was searching about simple harmonic motion, Wikipedia defined it as, "In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the accelerati...

Website writes The system is the tightrope walker, and the only external forces acting on him are his weight $W$ and the two tensions $T_L$ (left tension) and $T_R$ (right tension), as illustrated To be precise isn't TL and TR acting on the rope rather than the man? To calculate the tension we...

I was studying about the arrangements of orbitals in an atom and saw a simulation of the arrangement and that some area of a smaller orbital such as a 1s is contained inside a bigger orbital of 2s (a similar also happens in bonding as well when the orbitals overlap). So, I have a question regardi...